Many of the exterior shots of Tony's home or other areas show mountains or hills in the background. Florida, and southeast Texas where the astronauts actually lived, were as flat as a pancake, especially around Cape Kennedy and Cocoa Beach where the Nelsons are supposed to live.
The Roger Healy character was supposed to be an Army officer, but in the 1960's all astronauts had to be highly qualified pilots with long experience in high-performance jet aircraft. The Army did not (and does not) have any such aircraft, so all astronauts came from the Air Force, Navy, or Marine Corps. In addition, according to Healy's uniform insignia, he was not even in Army aviation; he was in the Corps of Engineers.